XV Workshop on Philosophical Logic

August 5–7, 2026

IIF - SADAF - CONICET

Buenos Aires, Argentina

Paul Egré (IRL Crossing, CNRS)

Thomas Macaulay Ferguson (Rensselaer Polytechnic Institute, USA)

Ulf Hlobil (Concordia Univesrity, Canada)

Franci Mangraviti (ETH Zurich, Switzerland)

Alba Massolo (National University of Córdoba, Argentina)

Cláudia Nalon (Department of Computer Science, University of Brasília, Brazil)

Elena Wüllhorst (King's College London, UK)

Wednesday 05/08 (GMT-3)

14:00 – 15:00 Thomas Macaulay Ferguson: "n-Sided Consequence, n-Lateralism, and Suszko's Thesis"

15:10 – 16:10 Bruno Da Re: "Tableaux for metavalidity"

16:10 – 16:50 coffee break

16:50 – 17:50 Elena Wüllhorst: "An intuitionistic conditional for Kripke’s theory of truth"

18:00 – 19:00 Cláudia Nalon: "Efficient Theorem-proving for Modal Logics"

Thursday 06/08 (GMT-3)

15:00 – 16:00 Franci Mangraviti: "Formalism freeness and the nihilist attitude"

16:10 – 17:10 Paula Teijeiro: "Local bayesianism for local validity"

17:10 – 17:50 coffee break

17:50 – 18:50 Damián Szmuc: "Regular logical matrices as monoidal matrices"

19:00 – 20:00 Paul Egré: "Vagueness and Probabilistic Consequence"

20:00 and on Workshop Dinner

Friday 07/08 (GMT-3)

14:00 – 15:00 Alba Massolo: "Rethinking Evidence: Logical Intuitions in Methodological Anti-exceptionalism"

15:10 – 16:10 Edson Bezerra: "Modal Metainferential Hierarchies"

16:10 – 16:50 coffee break

16:50 – 17:50 Mauro Santelli: "Expressivism about Logical Vocabulary and the Philosophy of Language"

18:00 – 19:00 Ulf Hlobil: "Objects, Properties, and Rational Forms"

Edson Bezerra: "Modal Metainferential Hierarchies"

I first present modal logics based on the three-valued logics TS and ST (as developed in Bezerra, 2024). I show that these logics are compatible with self-reference procedures (Smorynski, 1980). Then I generalize Barrio, Pailos & Szmuc hierarchy of metainferences based on ST Li(Barrio et al., 2018) for the logics K, T, D, K4, S4 and S5 based on ST. Lastly, I present a tableau system for the hierarchy of metainferences based on these modal logics. (Joint work with Federico Pailos and Jonathan Erenfryd.)

Bruno Da Ré: "Tableaux for metavalidity"

In this talk, we present a series of instructions for building sound and complete tableaux systems for inferential logics based on non-deterministic valuations and for extending them with rules for metainferences, thus yielding metainferential tableaux systems capable of proving metainferences of any level n, by taking into account not only the local notion of metavalidity, but also the global notion, and possible combinations of local and global validity at different levels. This work generalizes our recent paper Bavosa Castro, A., Borzi, A., Da Ré, B., Roffé, A. J., & Toranzo Calderón, J. S. (2026). Tableaux for metainferential logics. Journal of Applied Non-Classical Logics , 36(1), 113-146. (Joint work with Agustina Borzi and Ariel Roffé.)

Thomas Macaulay Ferguson: "n-Sided Consequence, n-Lateralism, and Suszko's Thesis"

Suszko's reduction is a technique by which every Tarskian consequence relation can be given a two-valued (but possibly noncompositional) model theory. Certain generalizations have been offered (e.g. that non-transitive logics can be given a three-valued reduction). I will present results (primarily developed by my student, Jitka Kadlečíková) that allow a great deal of new generalizations when considering n-sided consequence relations. I will give our results concerning Suszko reductions of n-sided consequence and discuss some of the many philosophical and semantics questions that these results gesture towards.

Paul Egré: "Vagueness and Probabilistic Consequence"

In this paper we are interested in the exploration of probabilistic accounts of the logic of vagueness that would provide empirically motivated counterparts to the strict-tolerant account proposed in Cobreros et al. (2012). In Egré and Ripley (2024), we explored a family of probabilistic consequence relations that we called symmetric consequence: symmetric consequence, like strict-tolerant consequence, says that a sentence follows from a set of premises when for every probability distribution, if the probability of each premise meets a sufficiently high threshold, then the probability of the conclusion meets a dual lower threshold. Symmetric consequence coincides with classical logic at the maximum threshold 1, and only gradually approaches it at lower thresholds. In this talk we deal with symmetric consequence over a language incorporating similarity relations. We define a probabilistic version of the tolerance principle for vague predicates, and we show that the logic validates the tolerance principle in argument form, and also in conditional form, but not as a universally quantified principle. Like ST, symmetric consequence for vague predicates is nontransitive, and like ST it accounts for the ambivalence felt in borderline cases. However, it differs from ST by invalidating the adjunction rule and so by rejecting borderline contradictions. Despite that, symmetric consequence relation nicely accommodates the observation that our confidence in the tolerance principle itself depends on how closely similar the items of a sorites sequence are. (Joint work with Ellie Ripley.)

Ulf Hlobil: "Objects, Properties, and Rational Forms"

I first present an extension of Implication-Space Semantics (as developed in Hlobil and Brandom, 2025) that includes first order quantification. I then raise the question whether this theory is consistent with the idea that propositions are primary, relative to their non-propositional parts. I present an account of names and predicates in terms of assertoric sentences and their inferential roles. The account can be translated into an account of objects and properties in terms of worldly propositions (which are things that are made true or false by states) and the alethic modal relations among them. The account exploits symmetries of modal structures. In slogan form: properties are what is common among symmetric points in modal space; objects are what differs among symmetric points in modal space.

Franci Mangraviti: "Formalism freeness and the nihilist attitude"

Building on remarks by Gödel on computability, Juliette Kennedy presents the notion of formalism freeness as "the idea that certain canonical concepts and constructions are stable across a variety of conceptually distinct formalisations, so seemingly insensitive to perturbations of logic and syntax." This can manifest as logic-independence, i.e. "invariance under substitution of one of a class of logics, considered on a case by case basis" (as in the notion of set constructibility, where infinitely many logics between first- and second-order end up converging on one of two notions) and the giving of a purely mathematical definition of some prima facie logical notion (as in Birkhoff's characterization of axiomatizable classes of algebras as being closed under certain algebraic operations). Crucially, "formalism freeness is not an all or nothing affair, but a matter of degree."

While Kennedy focuses on classical mathematics and extended classical logics, I argue that formalism freeness can be a fruitful guiding principle for nonclassical logics, especially (but not only) when paired with what I call a nihilist attitude: this involves being open to all possible logics, with no pressure to choose between them, and never treating a law as valid in every possible context. The nihilist attitude is independently supported by the state of logic as a field, and by metaphysical, pragmatic, and ethical considerations. Looking at a variety of case studies from the inconsistent mathematics literature, I show that a search for formalism freeness is already implicit in much work being done, and point to several results which are best understood under this lens. My conclusion is that keeping an active eye for formalism freeness - both its failures and its successes - can have significant benefits, and in particular help defending the nihilist attitude from standard objections.

Alba Massolo: "Rethinking Evidence: Logical Intuitions in Methodological Anti-exceptionalism"

Anti-exceptionalism about logic (AEL) challenges the traditional view of logic as an a priori, foundational, and exceptional discipline, instead arguing for its continuity with the empirical sciences. A key distinction within this debate, advanced by Martin and Hjortland (2022, 2025), separates methodological AEL the claim that logical theories are evaluated like scientific ones—from evidential AEL, which maintains that the evidence for logical theories does not differ from that of the empirical sciences. Although these two dimensions are often treated as independent—permitting the use of scientific methodologies while retaining exceptional sources of evidence—this presentation challenges that assumption.

Focusing on logical intuitions, I argue that both predictivism and abductivism—the two main variants of methodological AEL—implicitly rely on theory-independent evidence to avoid justificatory circularity. Yet recent empirical research in cognitive science suggests that logical intuitions are neither a priori nor theory-independent; rather, they function as “educated guesses” shaped by formal education and expert practice. Consequently, logical intuitions cannot serve as the theory-neutral data that predictivism and abductivism require. Instead, I contend that logical intuitions, as experientially shaped and revisable, align far more naturally with a coherentist methodology such as reflective equilibrium. This approach explicitly accommodates bidirectional adjustment between inferential practices and logical principles. Thus, this presentation not only highlights a challenge for predictivists and abductivists but also outlines a constructive alternative for anti-exceptionalism.

Cláudia Nalon: "Efficient Theorem-proving for Modal Logics"

Modal logics have been extensively studied, as they can express non-trivial problems ranging from domains in Mathematics and Philosophy to the representation of computational systems. The implementation of reasoning engines for those logics is, therefore, highly desirable. However, the satisfiability problem for even the most basic of the multimodal logics, the modal logic Kn, is not tractable: local and global reasoning in the multiagent set are PSPACE-complete and EXPTime-complete, respectively. We are, thus, interested in calculi that can be effectively employed for reasoning within those logics in an efficient way. In this talk, we will discuss two different resolution-based calculi for the multimodal Kn with particular focus on the characteristics that have an impact on automatic theorem-proving. We will report on experimental results and the influence of proof strategies and processing techniques for both calculi, and how different techniques impact the efficiency of theorem-proving in practice.

Mauro E. Santelli: "Expressivism about Logical Vocabulary and the Philosophy of Language"

I analyze, firstly, the metaphilosophical demands that adopting a Logical Expressivist position in the Philosophy of Logic has on the Philosophy of Language, particularly in terms of the relationship between semantics and pragmatics and their relationship with logic. To do so, I will take as an example the three logical systems presented by Hlobil and Brandom (2025) that are meant to expand the repertoire of logical systems that meet the demands of Logical Expressivism. These demands fit a Philosophy of Language that is antithetical to representationalist semantics understood classically even though Brandom and other inferentialists have suggested that this need not be the case. I present the sketch for a compatibilist argument between inferentialist meta-semantics and traditionally understood as representationalist semantics with recent developments of formal semantics that are usually thought out to be representationalist to the core. This theoretical commitment can be considered as optional.

Damián Szmuc: "Regular logical matrices as monoidal matrices"

This presentation aims to show how regular logical matrices can be seen as a special instance of the monoidal matrices introduced by Cintula, Gil-Férez, Moraschini, and Paoli in 2019. For this purpose, we consider a regular logical matrix $R$, later discussing its monoidal matrix representation $M^{R}$, and finally introducing its induced hypermatrix $H^{M^{R}}$. We will ultimately be able to show that the Tarskian consequence relation $\vDash_{\rm R}$ over the Set-Formula framework is equivalent to the multiset deductive relation $\vDash_{\rm H^{M^{R}}}$ over the Multiset-Formula framework. To conclude, we ponder the prospects of generalizing these techniques to present monoidal and hypermatrix counterparts for p-, q-, and b-matrices. Among other things, this would suggest the possibility of producing, e.g. a monoidal p-matrix and a corresponding hyper p-matrix for the sequent calculus G3c, when rules are formulated over multisets.

Paula Teijeiro: "Local bayesianism for local validity"

Metainferences are a higher level relation of forcing between inferences instead of formulas. How to properly determine which of them are valid remains an open debate. One of the most widespread definitions in the run, what is called `local validity’, amounts to satisfaction preservation from premises to conclusion. Those who argue against this characterization claim that it lacks a proper interpretation, and therefore, that it is just a technical tool, neither principled nor philosophically interesting. In this work, we propose a way to understand local validity by means of an epistemic interpretation: we will take locally valid metainferences to be those which preserve certain kind of evidence.

Elena Wüllhorst: "An intuitionistic conditional for Kripke’s theory of truth"

A central problem for Kripke’s theory of truth is the availability of a mathematically strong conditional. This talk presents a consistent Kripke-style theory of truth with an added intuitionistic conditional. First, it constructs the semantic theory of truth in two-steps using an order-theoretic fixed-point result. The resulting fixed-point model successfully formulates the T-schema A ↔ T ⌜A⌝ for Kripke's original language with the conditional. Next, it presents an axiomatization of the semantic theory and analyses it with respect to adequacy requirements outlined in the literature (Fischer et al., 2015): similarity, soundness, proof-theoretic strength and N-categoricity. All criteria are shown to hold, including a relativized N-categoricity result. Thus, both the semantic and the axiomatic theory can be said to capture Kripke's original construction, while adding the expressive resources of the conditional.

Camillo Fiore (UBA/IIF-SADAF-CONICET)

Mariela Rubin (UBA/IIF-SADAF-CONICET)

Joaquín S. Toranzo Calderón (UTN/UBA/IIF-SADAF-CONICET)

Victor Valderrama (IIF-SADAF-CONICET)

This workshop is supported by a grant from  RC-CONICET 2026 (Scientific Meetings grant)

We are thankful for the support provided by IIF-SADAF-CONICET.